diff --git a/Math/Sym.hs b/Math/Sym.hs
--- a/Math/Sym.hs
+++ b/Math/Sym.hs
@@ -42,6 +42,10 @@
     , avoiders        -- :: Perm a => [StPerm] -> [a] -> [a]
     , av              -- :: [StPerm] -> Int -> [StPerm]
 
+    -- * Single point deletions
+    , del             -- :: Perm a => Int -> a -> a
+    , shadow          -- :: (Ord a, Perm a) => a -> [a]
+
     -- * Simple permutations
     , simple          -- :: Perm a => a -> Bool
 
@@ -54,7 +58,7 @@
 import Data.Ord (comparing)
 import Data.Monoid (Monoid(..))
 import Data.Bits (Bits, bitSize, testBit, popCount, shiftL)
-import Data.List (sort, sortBy)
+import Data.List (sort, sortBy, group)
 import Data.Vector.Storable (Vector)
 import qualified Data.Vector.Storable as SV (Vector, toList, fromList, fromListN, empty, map, (++))
 import qualified Math.Sym.Internal as I
@@ -303,6 +307,18 @@
 -- 
 av :: [StPerm] -> Int -> [StPerm]
 av ps = avoiders ps . sym
+
+
+-- Single point deletions
+-- ----------------------
+
+-- | Delete the element at a given position
+del :: Perm a => Int -> a -> a
+del i = generalize $ fromVector . I.del i .toVector
+
+-- | The list of all single point deletions
+shadow :: (Ord a, Perm a) => a -> [a]
+shadow w = map head . group $ sort [ del i w | i <- [0 .. size w - 1]]
 
 
 -- Simple permutations
diff --git a/Math/Sym/Internal.hs b/Math/Sym/Internal.hs
--- a/Math/Sym/Internal.hs
+++ b/Math/Sym/Internal.hs
@@ -82,6 +82,9 @@
     , stackSort
     , bubbleSort
 
+    -- * Single point deletions
+    , del
+
     -- * Bitmasks
     , onesCUInt
     , nextCUInt
@@ -473,6 +476,23 @@
 -- | One pass of bubble-sort.
 bubbleSort :: Perm0 -> Perm0
 bubbleSort = sortop c_bubblesort
+
+-- Single point deletions
+-- ----------------------
+
+-- | Delete the element at a given position
+del :: Int -> Perm0 -> Perm0
+del i u = runST $ do
+  let n = SV.length u
+  let j = (SV.!) u i
+  v <- MV.unsafeNew (n-1)
+  forM_ [0..i-1] $ \k -> do
+            let m = (SV.!) u k
+            MV.unsafeWrite v k (if m < j then m else m-1)
+  forM_ [i+1..n-1] $ \k -> do
+            let m = (SV.!) u k
+            MV.unsafeWrite v (k-1) (if m < j then m else m-1)
+  SV.unsafeFreeze v
 
 
 -- Bitmasks
diff --git a/sym.cabal b/sym.cabal
--- a/sym.cabal
+++ b/sym.cabal
@@ -1,5 +1,5 @@
 Name:                sym
-Version:             0.2
+Version:             0.2.1
 Synopsis:            Permutations, patterns, and statistics
 Description:         
   Definitions for permutations with an emphasis on permutation
diff --git a/tests/Properties.hs b/tests/Properties.hs
--- a/tests/Properties.hs
+++ b/tests/Properties.hs
@@ -153,6 +153,16 @@
 prop_ordiso2 =
     forAll perm2 $ \(u,v) -> u `Sym.ordiso` v  ==  (Sym.inverse u `Sym.act` v == Sym.idperm v)
 
+shadow :: Ord a => [a] -> [[a]]
+shadow w = nubSort . map normalize $ ptDeletions w
+    where
+      normalize u = [ (sort w)!!i | i <- st u ]
+      nubSort = map head . group . sort
+      ptDeletions [] = []
+      ptDeletions xs@(x:xt) = xt : map (x:) (ptDeletions xt)
+
+prop_shadow = forAll perm $ \w -> Sym.shadow w == shadow w
+
 segments :: [a] -> [[a]]
 segments [] = [[]]
 segments (x:xs) = segments xs ++ map (x:) (inits xs)
@@ -172,8 +182,7 @@
 simple :: Ord a => [a] -> Bool
 simple = null . properIntervals
 
-prop_simple =
-    forAll (resize 50 perm) $ \w -> Sym.simple w == simple w
+prop_simple = forAll (resize 50 perm) $ \w -> Sym.simple w == simple w
 
 prop_unrankPerm =
     forAll perm $ \w ->
@@ -308,6 +317,7 @@
     , ("inverse",                        check prop_inverse)
     , ("ordiso/1",                       check prop_ordiso1)
     , ("ordiso/2",                       check prop_ordiso2)
+    , ("shadow",                         check prop_shadow)
     , ("simple",                         check prop_simple)
     , ("unrankPerm",                     check prop_unrankPerm)
     , ("stackSort",                      check prop_stackSort)